A first course in analysis
著者
書誌事項
A first course in analysis
（Cambridge mathematical textbooks）
Cambridge University Press, 2018
- : hardback
大学図書館所蔵 件 / 全5件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references and index
Includes bibliographical references (p. [331]) and index
内容説明・目次
内容説明
This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the basics of differentiation and integration of functions of one and several variables, and covers the theorems of Green, Gauss, and Stokes. Minimal prerequisites are assumed, and relevant linear algebra topics are reviewed right before they are needed, making the material accessible to students from diverse backgrounds. Abstract topics are preceded by concrete examples to facilitate understanding, for example, before introducing differential forms, the text examines low-dimensional examples. The meaning and importance of results are thoroughly discussed, and numerous exercises of varying difficulty give students ample opportunity to test and improve their knowledge of this difficult yet vital subject.
目次
- 1. The real numbers
- 2. Differentiation
- 3. Integration
- 4. Sequences of functions
- 5. Metric and Euclidean spaces
- 6. Differentiation in higher dimensions
- 7. Integration in higher dimensions
- 8. Curves and surfaces
- 9. Differential forms.
「Nielsen BookData」 より